1. NSW Curriculum and Learning Innovation Centre Tinker with Tinker Plots Elaine Watkins, Senior Curriculum Officer, Numeracy

2. NSW Curriculum and Learning Innovation Centre Graphs in the curriculum Graphs play a significant role in the mathematics curriculum, providing visual means of presenting information. The visual representations provide numerical, pictorial, and statistical information by combining symbols, points, lines, numbers, shading and colour (Tufte, 1983) with the aim of conveying information quickly and efficiently. Students should have the experience to create graphs with and without technology, so that they can explain what they have created and draw conclusions from the representations.

3. NSW Curriculum and Learning Innovation Centre Comparison of Syllabus Outcomes 2002 Syllabus – Key ideas Statistics and probability Draft Syllabus Chance and Data Early Stage 1Stage 1Early Stage 1Stage 1 Collect data about students & their environment Gather & record data using tally marks Uses concrete materials and/or pictorial representations to support conclusions Supports conclusions by explaining or demonstrating how answers were obtained (data1 & data 2) Display the data using concrete materials & pictorial representations Use objects or pictures as symbols to represent other objects, using one- to-one correspondence Organise actual objects or pictures of the objects into a data display Represents data & interprets data displays made from objects & pictures Gathers & organises data, representing data in column & picture graphs, & interprets the results (data 1 & data 2) Uses objects, diagrams & technology to explore mathematical problems (data 2) Interpret data displays made from objects and pictures Interpret information presented in picture graphs & column graphs Recognise the element of chance in familiar daily events Use familiar language to describe the element of chance Describes mathematical situations & methods using everyday & some mathematical language, actions, materials, diagrams and symbols (data 1 & data 2) Describes mathematical situations using everyday language, actions, materials and informal recordings

4. NSW Curriculum and Learning Innovation Centre Comparison of Syllabus Outcomes 2002 Syllabus – Key ideasDraft Syllabus Stage 2Stage 3Stage 2 Data 1 & 2 Stage 3 Data 1 & 2 Chance and data Conduct surveys, classify & organise data using tables Draw picture, column, line & divided bar graphs using scales of many-to-one correspondence Statistics & probability Uses appropriate terminology to describe, & symbols to represent, mathematical ideas Describes & represents mathematical situations in a variety of ways using mathematical terminology & some conventions Construct vertical & horizontal column graphs& picture graphs Read & interpret sector (pie) graphs Selects & uses appropriate mental or written strategies, or technology to solve problems Gives a valid reason for supporting one possible solution over another Interpret data presented in tables, column graphs and picture graphs Read & interpret graphs with scales of many-to-one correspondence Checks the accuracy of a statement & explains the reasoning used Uses appropriate data collection methods, constructs & interprets data displays & analyses sets of data Determine the mean (average) for a small set of data Selects appropriate data collection methods & constructs, compares & interprets data displays Explore all possible outcomes in a simple chance situation Conduct simple chance experiments Collect data & compare likelihood of events in different contexts Assign numerical values to the likelihood of simple events occurring Order the likelihood of simple events on a number from 0 to 1

5. NSW Curriculum and Learning Innovation Centre What is Tinker Plots? Tinker Plots is a data analysis program designed to enable students in grades 4–8 to get excited about what they can learn from data. The students will analyse data by creating colourful visual representations that will help the students make sense out of real data and recognize patterns as they unfold. Students can use Tinker Plots to produce reports that include graphs, along with text that explains their findings and even photos they take or locate on the Internet. Students can manipulate data and learn what the relationships mean.

6. NSW Curriculum and Learning Innovation Centre How can Tinker plots be used? Students can use Tinker plots to: construct dot plots for numerical data consider the data type to determine & draw the most appropriate display for the data, including column graphs, dot plots and line graphs name & label the horizontal & vertical axes when constructing graphs tabulate collected data, including numerical data with & without the use of digital technologies such as spreadsheets discuss & draw conclusions from different data displays interpret information presented in two-way tables create a two-way table to organise data involving two categorical variables interpret & compare different displays of the same data interpret data representations found in digital media and in factual texts.

7. NSW Curriculum and Learning Innovation Centre What is a stacked dot plot? A stacked dot plot is a way of representing numerical data. They are ideal for making comparisons of data.

8. NSW Curriculum and Learning Innovation Centre Table group task using a stacked dot plot As a table group collect data to create a stacked dot plot. Write down your height (estimate if not known), and shoe size. As a whole group, determine an appropriate scale for creating a stacked dot plot. Use a paper streamer for the scale and the coloured dots to create a stacked dot plot to represent the data you collected. Label the stacked dot plot. What questions could you ask about your graph and data?

9. NSW Curriculum and Learning Innovation Centre Features of a stacked dot plot Features include: An automatic sorting of data - once the axis is chosen the data points can be plotted in any order but are actually sorted by the plotting process. A good choice of scale in a dot plot can make the shape of the data clearer Easy identification of the range and highlighting of extreme values (‘outliers’). Reveals any peaks and/or mode/s in the data.

10. NSW Curriculum and Learning Innovation Centre Looking at data in Tinker Plots

11. NSW Curriculum and Learning Innovation Centre Importing data from Excel spreadsheet

12. NSW Curriculum and Learning Innovation Centre Stacked dot plots - teaching implications Use real data, relevant to the students Students need to determine an appropriate scale from the data collected. Identify the lowest score and the highest score. In a stacked dot plot, the dots must align vertically and horizontally. Example of a poor stacked dot plot Stacked dot plots only give a good pictorial representation of frequency when the 'dots' are aligned.

13. NSW Curriculum and Learning Innovation Centre Stacked dot plots - teaching implications The graph and the axis need to be labelled. Is the data accurate? Look at outliers. Students should be able to describe what the stacked dot plot shows about the data Introduce statistical terminology to assist students to describe their data (e.g. mode, median, range, mean, outlier) When comparing two stacked dot plots, have the same range and scale on the axis

14. Resource to support the statistics and probability strand This report focuses on the application of graphs for portraying data, and their potential as instruments for reasoning about quantitative information. Available from http://www.curriculumsupport.e ducation.nsw.gov.au/primary/m athematics/resources/data/ind ex.htmhttp://www.curriculumsupport.e ducation.nsw.gov.au/primary/m athematics/resources/data/ind ex.htm